Satellite constellations are a part of our daily lives, from Direct TV to our cell phones and car navigation. We present the rudiments of constellation design to familiarize the readers with some of the methods, issues, and concerns of this field. The use of circular orbits, elliptical orbits, synchronous orbits, combined with dynamical effects of Earth's J2 gravitational harmonics produce an array of constellations with specific properties to support various mission constraints. A key point is that constellation design is not the mere repetition of the template of a satellite orbit. The aggregate of satellites and orbits present a totally new systems problem with a combinatorial growth in complexity even for the most elementary of analysis questions. The fundamental performance metric is the constellation geometric coverage statistics. Ergodic theory, the multiresolution visual calculus, and dynamical systems theory are some new approaches to the constellation design problems. New infrastructures and new paradigms are required to further develop this technology.